The projack: A resampling approach to correct for ranking bias in high-Throughput studies

Abstract

The problem of ranked inference arises in a number of settings, for which the investigator wishes to perform parameter inference after ordering a set of $m$ statistics. In contrast to inference for a single hypothesis, the ranking procedure introduces considerable bias, a problem known as the "winner's curse" in genetic association. We introduce the projack (for Prediction by Re-Ordered Jackknife and Cross-Validation, $K$-fold). The projack is a resampling-based procedure that provides low-bias estimates of the expected ranked effect size parameter for a set of possibly correlated $z$ statistics. The approach is flexible, and has wide applicability to high-dimensional datasets, including those arising from genomics platforms. Initially, motivated for the setting where original data are available for resampling, the projack can be extended to the situation where only the vector of $z$ values is available. We illustrate the projack for correction of the winner's curse in genetic association, although it can be used much more generally.